In the given figure, AB and AC are tangents to a circle with center 0 and radius 8 cm. If OA = 17 cm, then the length of AC (in cm) is
As AB is tangent to the circle at point B
OB ⏊ AB
[Tangents drawn at a point on circle is perpendicular to the radius through point of contact]
In right angled triangle AOB,
By Pythagoras Theorem,
[i.e. (Hypotenuse)2 = (Base)2 + (Perpendicular)2 ]
(OA)2 = (OB)2 + (AB)2
(17)2 = (8)2 + (AB)2
[As OA = 17 cm is given and OB is radius]
289 = 64 + (AB)2
(AB)2 = 225
AB = 15 cm
Now, AB = AC [Tangents drawn from an external point are equal]
∴ AC = 15 cm
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